The purpose of supervised learning with temporal encoding for spiking neurons is to make the neurons emit arbitrary spike trains in response to given synaptic inputs.However

due to the discontinuity in the spike process

the formulation of efficient supervised learning algorithms for spiking neurons is difficult and remains an important problem in the research area.Based on the definition of kernel functions for spike trains

this paper proposes a new supervised learning algorithm for spiking neurons with temporal encoding.The learning rule for synapses is developed by constructing the multiple spikes error function using spike train kernels

and its learning rate is adaptively adjusted according to the actual firing rate of spiking neurons during learning.The proposed algorithm is successfully applied to various spike trains learning tasks

in which the desired spike trains are encoded by Poisson process or linear method.Furthermore

the effect of different kernels on the performance of the learning algorithm is also analyzed.The experiment results show that our proposed method has higher learning accuracy and flexibility than the existing learning methods

so it is effective for solving complex spatio-temporal spike pattern learning problems.